On Sunday, July 27, 2014 8:40:50 PM UTC-7, Stephen Kauffman wrote:
>
> Thanks for your help but I think I need more. I've written some code for a
> somewhat general case of n orthogonal generators and an arbitrary diagonal
> metric and I think I've generated the correct 16x16 matrices for my n=4
> case.
>
I think you're mainly running into python syntax issues here. For the most
part, whenever you use "exec" in a computer algebra package, you're doing
something wrong. There is probably a better way of passing around
information (mind you, sometimes there's not. You're still doing something
wrong, but the package might not give you the tools to do it right).
> When I finish running the .sage file and return to sage I execute
>
> F = PRGA.monoid()
> MyStr=str(PRGA.gens())
> MyStr=MyStr[1:len(MyStr)-1]
> exec MyStr+' = F.gens()'
> ST.<g0,g1,g2,g3>=FreeAlgebraQuotient(PRGA,MyList6,mats)
> ST
> Free algebra quotient on 4 generators ('g0', 'g1', 'g2', 'g3') and
> dimension 16 over Rational Field
>
> but when I do
>
> g3*g3 # or ST.gen(3)*ST.gen(3)
> AttributeError: 'FreeAlgebra_generic_with_category.element_class' object
> has no attribute '_element_list'
>
I can't reproduce this error because you're not telling what MyList6 and
mats are. If I set
sage: g0,g1,g2,g3 = F.gens()
sage: MyList6 = [ F(1), g0, g1, g2, g3, g0*g1, g0*g2, g0*g3, g1*g2, g2*g3,
g3*g1, g0*g1*g2*g3*g0, g0*g1*g2*g3*g1, g0*g1*g2*g3*g2, g0*g1*g2*g3*g3,
g0*g1*g2*g3]
sage: mats=[matrix(QQ,16,16,1) for j in range(4)]
sage: ST.<g0,g1,g2,g3>=FreeAlgebraQuotient(PRGA,MyList6,mats)
sage: ST.gen(3)*ST.gen(3)
g3
I get no error (I do get a rather nonsensical result because I initialized
the matrices to nonsense).
> Further when I try to automate with the generated string MyStr='g0, g1,
> g2, g3' and within the .sage file
>
> exec 'ST.<'+MyStr+'> = FreeAlgebraQuotient(PRGA,MyList6,mats)'
>
> Traceback (most recent call last):
> File "<string>", line 1
> ST.<g0, g1, g2, g3> = FreeAlgebraQuotient(PRGA,MyList6,mats)
> ^
> SyntaxError: invalid syntax
>
That's because "exec" is just python's "exec" and you're giving syntax that
needs sage's preparser. The ST.<g0> syntax is not valid python. To see how
it converts:
sage: preparse("ST.<g0,g1,g2,g3> = FreeAlgebraQuotient(PRGA, mons, mats)")
"ST = FreeAlgebraQuotient(PRGA, mons, mats, names=('g0', 'g1', 'g2',
'g3',)); (g0, g1, g2, g3,) = ST._first_ngens(4)"
which also helps you for your next error:
> If I try:
>
> ST=FreeAlgebraQuotient(PRGA,MyList6,mats, names='g0, g1, g2, g3') # or
> anything else I try in names
>
> Traceback (most recent call last):
> ValueError: first letter of variable name must be a letter
>
As the preparse command shows, it should work if you set names to a tuple
(really, an iterable) of strings. A nasty design choice is that strings
themselves are iterables, which produce their individual characters. Compare
sage: [x for x in ('g0', 'g1', 'g2', 'g3')]
['g0', 'g1', 'g2', 'g3']
sage: [x for x in "g0, g1, g2, g3"]
['g', '0', ',', ' ', 'g', '1', ',', ' ', 'g', '2', ',', ' ', 'g', '3']
Hence the error message: '0' is not a valid generator name.
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